A company sells meal kits. Suppose that 70% of the first-time customers who order a vegetarian meal will order again, while 65% of the first-time customers who order a gluten-free meal will order again. The company takes
separate random samples of 50 first-time customers who order each kind of meal. The company will then look at
the difference (vegetarian – gluten free) between the proportions of customers who order again in each
sample.
What will be the shape of the sampling distribution of the difference in sample proportions, and why?

A

Approximately normal, because we expect 35 successes and 15 failures from vegetarian orders, and 32.5 and 17.5 from gluten-free orders, and all of these counts are at least 10

Step-by-step explanation: Khan Answer

For vegetarian orders 70% order again, so with a sample size of 50 we will have an estimated 35 people order again: This results in 35 successes and 15 failures. For gluten-free orders 65% order again, so with a sample size of 50 we will have an estimated 32.5 people order again: This results in 32.5 successes and 15 failures. Because these are all greater than 10, we can assume normality.

x= 149. 24+7=31. 180-31=149

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